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Sarcomeric Pattern Formation by Actin Cluster Coalescence
Figure 3
Sarcomeric ordering in the presence of myosin.
A. Simulation snap-shots showing the emergence of sarcomeric order in an acto-myosin bundle ( single actin filaments: blue and red, myosin filaments: magenta, plus-end crosslinker connecting actin filament plus ends belonging to one cluster : green). Actin filaments can interact if their projections on the bundle axis overlap. Additionally, bipolar myosin filaments (magenta) dynamically attach to actin filaments in a polarity-specific manner, thus acting as a second set of active crosslinkers. Different vertical positions of the filaments are indicated solely for visualization purposes. Initially, filament positions are random (
). After a transient period during which clusters of crosslinked actin filaments form and coalesce (
), a stable configuration is established characterized by a periodic pattern of actin clusters interspersed by bands of aligned myosin (
). To characterize sarcomeric order in these simulated bundles, we compute the structure factor 
as defined in the main text (blue curves in lower panel, simulation time 
, respectively). The height of the principal Bragg peak (red circle) defines the sarcomeric order parameter 
. The active myosin force that tends to oppose sarcomeric ordering was chosen as 
, measured in units of 
. An animated version of this simulation can be found as Video S1 available online as Supplementary Information. B. Illustration of the ‘actin conveyer belt’ mechanism: Actin filaments that are grafted at their plus-end by a processive crosslinker have to polymerize against the crosslinker (that acts as an obstacle) and are pushed backwards in a form of local retrograde flow. Myosin filaments interacting with these treadmilling actin filaments are transported away from the cluster center provided that the actin treadmilling speed exceeds the active myosin walking speed. C. Myosin filaments that are attached to actin filaments from two neighboring clusters serve as an active crosslinker and mediate repulsive forces between the two clusters due to the difference in the actin polymerization forces and the myosin active forces, see also SI text S1. D. Myosin active force slows-down sarcomeric ordering: The inset shows the time-course of the sarcomeric order parameter 
(blue,mean
s.e.,
) for 
, together with a fit of simulation results to an exponential saturation curve 
(red) that allows us to extract a time-scale 
of sarcomeric ordering. The main plot shows this time-scale 
as a function of myosin force 
; 
diverges as 
approaches a critical value 
. For myosin forces that are larger the critical value 
, sarcomeric order is not established. Instead, myosin forces facilitate the coalescence of crosslinked actin clusters into a small number of very large clusters (not shown), similar to the case shown in figure 2B without friction.
doi: https://doi.org/10.1371/journal.pcbi.1002544.g003